nice post, chris.
isn't the inverse problem also the basis for a lot of crypto? vis-a-vis
a "one way function":
http://www.c3.lanl.gov/mega-math/gloss/compute/oneway.html
douglas
Christopher Weare wrote:
> You do not have enough information from the data to actually separate
> the instruments by looking at the spectrum. What you are attempting to
> perform is a member of the nasty inverse problem class. A very simple
> example:
>> Given 42, determine uniquely the two numbers added together to produce
> that result.
>> While it is simple enough to calculate 40 + 2 = 42, the inverse problem,
> 42 = ? + ?, can not be solved uniquely with the information given.
>> To solve the audio inversion problem you must have an a priori model for
> the spectrum each source will produce. To make this remotely tractable
> you need to have some clue as to what instruments are even present in
> the first place.
>> The brain is able to localize so well because it does have internal
> models of expected sounds it uses to solve the inverse problem. The
> brain uses a similar tact to solve the equally vexing inverse optics
> problem.
>> But don't feel discouraged. Inverse problems are probably some of the
> most difficult challenges left in engineering so it will probably take
> some extra effort to make some progress.
>>> Have fun,
> -chris
>>>>>> -----Original Message-----
> From: Keith Handy [mailto:keith at indierecords.com]
> Sent: Monday, June 10, 2002 2:45 PM
> To: music-dsp at shoko.calarts.edu> Subject: [music-dsp] Wondering if this has been tried yet . . .
>> Just a brainstorm I had the other night -- if you continuously analyze
> the
> full audio spectrum of a stereo signal, couldn't you break the signal
> down
> into all its frequency components and figure out where they're all
> coming
> from in the stereo field? And in doing so, couldn't you conceiveably
> identify and isolate the "center material" (or material panned to any
> given
> location) in a stereo mix, and filter out anything that is known to be
> panned elsewhere (in the same way that noise can be filtered out using a
>> noise profile)?
>> (Or maybe one would use resynthesis instead of filtering, or even some
> "intelligent" combination of both.)
>> I'm thinking a kind of "inverted Karaoke" effect where instead of just
> dumbly cancelling out one location, you actually could isolate a
> position
> in the field -- and if this were possible, it follows that you could
> break
> a stereo field up into *several* independent tracks, though I realize
> there
> are probably a lot of good reasons why this wouldn't work spectacularly
> well.
>> Maybe you would have to analyze phase relationships between the channel,
> in
> case there's energy in the same band coming from two instruments panned
> opposite each other. Or maybe it would be a matter of analyzing (L-R)
> and
> using that profile to filter (L+R).
>> I'm thinking this is one of those things that would be heavily flawed,
> in
> the same way that time stretching is flawed -- but I'd be interested to
> hear what would come out regardless. I'm also sure I'm not the first to
>> think of it, as I never am, but I figure some of you on this list would
> know more about the logistics of practical implication. It's beyond my
> skill level to actually attempt this, but it's been a fun thing to think
> about.
>> -Keith
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